I’ll be in Sydney next week for a holiday vacation. Can I go to New Zealand without any procedures?

No, you can’t travel without any formalities to New Zealand; to do so you would need to be an Australian citizen, a holder of an Australian permanent residence permit, or must have a current Australian resident return visa. Just holding an Australian visa does not exempt from the New Zealand visa requirement.
http://glossary.immigration.govt.nz/VisaFreeCountries.htm ..